Question Detail

217 * 217 + 183 * 183

70578
82578
80578
80568

Answer: Option C

Explanation:

\begin{aligned}
\frac {1}{2}\times 2(a^2 + b^2) = \frac {1}{2} \times [(a + b)^2 + (a - b)^2]
\end{aligned}
\begin{aligned}
= \frac {1}{2} \times [(217 + 183)^2 + (217 - 183)^2] = 80578
\end{aligned}

1. 587 * 999 = ?

586411
586413
486411
486413

Answer: Option B

Explanation:

Trick: 587 * (1000 - 1) = 587000 - 587 = 586413

2. Find the unit digit in \begin{aligned}
(544)^{102} + (544)^{103}
\end{aligned}

Answer: Option C

Explanation:

Required digit is = \begin{aligned}
(4)^{102} + (4)^{103} \end{aligned}
as \begin{aligned} (4)^2 \end{aligned} gives unit digit 6 so \begin{aligned} (4)^{102} \end{aligned} unit digit is 6 and \begin{aligned} (4)^{103} \end{aligned} unit digit is, unit digit of \begin{aligned} 6 \times 4 \end{aligned}= 4, so answer will be unit digit of 6 + 4 = 0

3. The greatest number by which the product of three consecutive multiples of 3 is always

Answer: Option C

Explanation:

3*6*9 = 162

4. All prime numbers are odd numbers

True
False

Answer: Option B

Explanation:

It is false, 2 is an even number

5. A number when divided by the sum of 555 and 445 gives two times their difference as quotient and 30 as remainder. The number is

22030
220030
23030
24030

Answer: Option B

Explanation:

(555 + 445) * 2 * 110 + 30 = 220000 + 30 = 220030

Question Detail

217 * 217 + 183 * 183

1. 587 * 999 = ?

2. Find the unit digit in \begin{aligned} (544)^{102} + (544)^{103} \end{aligned}

3. The greatest number by which the product of three consecutive multiples of 3 is always

4. All prime numbers are odd numbers

5. A number when divided by the sum of 555 and 445 gives two times their difference as quotient and 30 as remainder. The number is

2. Find the unit digit in \begin{aligned}
(544)^{102} + (544)^{103}
\end{aligned}